Some memory cells, such as one-time-programmable (OTP) memory cells, cannot be pre-tested to determine whether they can reliably stored data. As a result, redundancy mechanisms can be built-into a memory device, such that, if there is an error in field-programming memory cells in a normal data storage area in the memory device, the data can instead be written to a repair area in the memory device. That way, despite such errors, a data storage system can read and write to the memory device without losing any data. In some memory arrays, data that was successfully stored in a row in a memory array can become unreadable after an adjacent row is written to. For example, in a memory array with antifuse-based memory cells, a leakage path can be caused by a defect that resides in a location that is not electrically visible until the rupture of the antifuse. Once the antifuse is ruptured and a filament is formed, this defect can provide a short circuit between the row being programmed and one or both of its neighboring rows, rendering previously-stored data in a neighboring row unreadable. In such a situation, in addition to repairing the data in the row where the defect was detected, the redundancy mechanism can repair the previously-stored data from the neighboring row. This and other related redundancy mechanisms are described in U.S. Pat. No. 7,212,454.